On evaluation of transverse spin fluctuations in quantum magnets

A numerical method is described for evaluating transverse spin correlations in the random phase approximation. Quantum spin-fluctuation corrections to sublattice magnetization are evaluated for the antiferromagnetic ground state of the half-filled Hubbard model in two and three dimensions in the whole U/t range. Extension to the case of defects in the AF is also discussed for spin vacancies and low-U impurities. In the limit, the vacancy-induced enhancement in the spin fluctuation correction is obtained for the spin-vacancy problem in two dimensions, for vacancy concentration up to the percolation threshold. For low-U impurities, the overall spin fluctuation correction is found to be strongly suppressed, although surprisingly spin fluctuations are locally enhanced at the low-U sites. Received 27 April 1998 and Received in final form 13 August 1998     

Ferrimagnetic ground state of a phenylene polymer with organic radicals

A ferrimagnetic polymer with m-phenylene skeleton as coupling unit is studied with the Hubbard model in the self-consistent mean-field theory. The ferrimagnetic ground state with a total spin S = 1 per unit cell is obtained and originates from the antiferromagnetic correlations between the nearest neighbors. If the on-site electron-electron repulsions at the radical sites and at the phenylene ring sites are different, the gap in energy band structure may disappear and the ferrimagnetic ground state becomes unstable. The charge density and spin density can transfer between the radical sites and the phenylene ring sites due to the competition between the hopping integral and the on-site repulsion at different sites. Received 15 July 2002 Published online 31 December 2002     

Coulomb repulsion versus Hubbard repulsion in a disordered chain

We study the difference between on site Hubbard and long range Coulomb repulsions for two interacting particles in a disordered chain. The system size L (in units of the lattice spacing) is of the order of the one particle localization length and the energies are taken near the band center. In the two cases, the limits of weak and strong interactions are characterized by uncorrelated energy levels and are separated by a crossover regime where the states are more extended and the spectra more rigid. U denoting the interaction strength and t the kinetic energy scale, the crossovers take place for interaction energy to kinetic energy ratios U/t and U/(2tL) of order one, for Hubbard and Coulomb repulsions respectively. While Hubbard repulsion can only yield weak critical chaos with intermediate spectral statistics, Coulomb repulsion can drive the two particle system to quantum chaos with Wigner-Dyson spectral statistics. The interaction matrix elements are studied to explain this difference. Received 21 March 2000 and Received in final form 5 February 2001     

A numerical study of the formation of magnetisation plateaus in quasi one-dimensional spin-1/2 Heisenberg models

We study the magnetisation process of the one-dimensional spin-1/2 antiferromagnetic Heisenberg model with modulated couplings over j=1,2,3sites. It turns out that the evolution of magnetisation plateaus depends on j and on the wave number q of the modulation according to the rule of Oshikawa et al. A mapping of two- and three-leg zig-zag ladders on one-dimensional systems with modulated couplings yields predictions for the occurrence of magnetization plateaus. The latter are tested by numerical computations with the DMRG algorithm. Received 14 October 1999 and Received in final form 6 January 2000     

Spin-wave renormalization by mobile holes in a two-dimensional quantum antiferromagnet

The coupling of antiferromagnetic spin excitations and propagating holes has been studied theoretically on a square lattice in order to investigate the dependence of antiferromagnetic order on hole doping, being of relevance, e.g., for the Cu–3 d⁹ system in antiferromagnetic CuO₂-planes of high-T_c superconductors. An effective Hamiltonian has been used, which results from a 2D Hubbard model (hopping integral t) with holes and with strong on-site Coulomb repulsion U. Bare antiferromagnetic excitations and holes with energies of the same order of magnitude t²/U are interacting via a coupling term being proportional to t and allowing holes to hop by emitting and absorbing spinwaves. In terms of a self-consistent one-loop approximation the renormalization of the spectral function both of holes and antiferromagnetic spin excitations are calculated.     

Local environment and electron correlation effects on the magnetic properties of clusters

The electronic and magnetic properties of clusters are investigated in the framework of the Hubbard model by treating electron correlations effects in a saddle-point slave-boson approximation. The size dependent single-particle spectrum is calculated using a third moment real-space expansion of the local density of states. Results for the magnetic moments, magnetic order, average number of double occupations and hopping renormalizations are given as a function of the local coordination number z, for different representative values of the Coulomb interaction strength U/t and band filling n. Several transitions between paramagnetic, ferromagnetic and antiferromagnetic behaviors are obtained as a function of z. The environment dependence of the magnetic behavior and of the degree of electron delocalization is analyzed. Advantages and limitations of the present approach are discussed. Received: 8 January 1998 / Revised: 22 June 1998 / Accepted: 6 August 1998     

Nonlinear electrostatic response of strongly correlated one-dimensional electron systems

We investigate the nonlinear response of the strongly correlated one-dimensional electron systems to the static electric field with using the one-dimensional Hubbard model in the half-filled case. We adopt the variational Monte Carlo method with the Gutzwiller wave function to describe the strong correlation effects. In the weak correlation region U/t≤4, where U is the one-site Coulomb repulsion energy and t is the transfer integral between the nearest neighbor sites, the response can be described within the band picture, and the third order nonlinear susceptibility χ⁽³⁾ increases slowly with increasing U/t. For U/t≤4, χ⁽³⁾ increases rapidly with increasing U/t, and χ⁽³⁾ at U/t=10 is more than ten times larger than that at U/t=2. This large value of χ⁽³⁾ originates from the exotic properties of carriers in the strongly correlated one-dimensional electron systems.     

Andreev-Lifshitz supersolid revisited for a few electrons on a square lattice II

In this second paper, using N = 3 polarized electrons (spinless fermions) interacting via a U/r Coulomb repulsion on a two dimensional L×L square lattice with periodic boundary conditions and nearest neighbor hopping t, we show that a single unpaired fermion can co-exist with a correlated two particle Wigner molecule for intermediate values of the Coulomb energy to kinetic energy ratio r _s = UL/(2t ). This supports in an ultimate mesoscopic limit a possibility proposed by Andreev and Lifshitz for the thermodynamic limit: a quantum crystal may have delocalized defects without melting, the number of sites of the crystalline array being smaller than the total number of particles. When L = 6, the ground state exhibits four regimes as r_s increases: a Hartree-Fock regime, a first supersolid regime where a correlated pair co-exists with a third fully delocalized particle, a second supersolid regime where the third particle is partly delocalized, and eventually a correlated lattice regime. Received 22 October 2002 Published online 23 May 2003 RID="a" ID="a"e-mail: jpichard@cea.fr     

Study on the ferrimagnetic ground state of a phenylene molecule chain

The properties of the ferrimagnetic ground state of an m  -phenylene molecule chain are studied with the Hubbard model. Within mean-field theory, the ferrimagnetic ground state with a total spin S=1$S=1$ per unit cell is obtained. The result shows that if the on-site electron–electron repulsion U   at the radical sites and _U0$U_0$ at the phenylene ring sites are different, the energy gap may disappear and the ferrimagnetic ground state becomes unstable. The spin configuration exhibits that the ferrimagnetic ground state results from the antiferromagnetic correlations between the nearest neighbors. Due to the cooperation and competition between the hopping integral and the on-site repulsion at different sites, the charge density and spin density can transfer between the radical sites and the phenylene ring sites.     

Quantum spin-{3 \over 2} models on the Cayley tree - optimum ground state approach

We present a class of optimum ground states for quantum spin- models on the Cayley tree with coordination number 3. The interaction is restricted to nearest neighbours and contains 5 continuous parameters. For all values of these parameters the Hamiltonian has parity invariance, spin-flip invariance, and rotational symmetry in the xy-plane of spin space. The global ground states are constructed in terms of a 1-parametric vertex state model, which is a direct generalization of the well-known matrix product ground state approach. By using recursion relations and the transfer matrix technique we derive exact analytical expressions for local fluctuations and longitudinal and transversal two-point correlation functions. Received 1 March 1999     

Statistics of inter-particle distances and angles in plasmas

Accurate treatment of the plasma density effects requires a detailed knowledge of the spatial distribution of individual ions around a test ion. In the present work, rigorous expressions are derived for the main 2- and 3-particle spatial distribution functions involving the nearest neighbor (NN) and the next-nearest neighbor (NNN) ions. These expressions, valid for both ideal and nonideal plasmas, present the distributions as functionals of the potentials U _NN and U _NNN at the nearest and next-nearest ion locations. All of the distribution functions except one are derived and discussed in the present work for the first time ever. For utilization of our results in practical calculations, we suggest semi-empirical expressions for U _NN and U _NNN in the ion-ion coupling parameter range 0 ?Γ < 1. In order to test the accuracy of our expressions for U _NN and U _NNN we conduct Molecular Dynamics (MD) simulations. The simulations utilize the pure Coulomb particle-particle interaction potentials, regularized at close range to avoid classical Coulomb collapse, and are free from the assumptions made to find U _NN and U _NNN. Thus, the results of the MD simulations provide an independent test of our theoretical results. Excellent agreement has been found between the results of the theory and of the MD simulations. Finally, we outline the implications of the present findings on the problem of tunneling and charge exchange in dense plasmas. Received 27 October 2000 and Received in final form 30 January 2001     

Destruction of the Fermi surface due to pseudogap fluctuations in strongly correlated systems

We generalize the dynamical-mean field theory (DMFT) by including into the DMFT equations dependence on the correlation length of the pseudogap fluctuations via the additional (momentum dependent) self-energy Σ_k. This self-energy describes nonlocal dynamical correlations induced by short-ranged collective SDW-like antiferromagnetic spin (or CDW-like charge) fluctuations. At high enough temperatures, these fluctuations can be viewed as a quenched Gaussian random field with finite correlation length. This generalized DMFT + Σ_k approach is used for the numerical solution of the weakly doped one-band Hubbard model with repulsive Coulomb interaction on a square lattice with nearest and next nearest neighbor hopping. The effective single impurity problem is solved by using a numerical renormalization group (NRG). Both types of strongly correlated metals, namely, (i) doped Mott insulator and (ii) the case of the bandwidth W ? U (U-value of local Coulomb interaction) are considered. By calculating profiles of the spectral densities for different parameters of the model, we demonstrate the qualitative picture of Fermi surface destruction and formation of Fermi arcs due to pseudogap fluctuations in qualitative agreement with the ARPES experiments. Blurring of the Fermi surface is enhanced with the growth of the Coulomb interaction.     

On the ground state of the half-filled Hubbard model

We calculate the ground state of the half-filled Hubbard model and its energy by starting from a spindensity wave approximation and improving it by incorporating transverse spin fluctuations. The calculations are done by employing a projection method. The quality of the proposed approximation is particularly high for intermediate and large Coulomb repulsionU, where it exceeds considerably e.g. that of the Gutzwiller projected spin-density wave state. To ordert ²/U (wheret is the hopping matrix element), our approximation is shown to be equivalent to a recent Coupled Cluster calculation for the Heisenberg antiferromagnet. Finally we show how to ordert ²/U the linear spin-wave approximation for the Heisenberg antiferromagnet may be obtained.     

Superconductivity in weakly correlated electron systems

We study the influence of the short-ranged Hubbard correlation U between the conduction electrons on the Cooper pair formation in normal (s-wave) superconductors. The Coulomb correlation is considered within the standard second order perturbation theory, which becomes exact in the weak coupling limit but goes beyond the simple Hartree-Fock treatment by yielding a finite lifetime of the quasiparticles at finite temperature. An attractive pairing interaction V, which may be mediated by the standard electron-phonon mechanism, is considered between nearest neighbor sites. A critical value for the attractive interaction is required to obtain a superconducting state. For finite temperature a gapless superconductivity is obtained due to the finite lifetime of the quasiparticles, i.e. the Coulomb correlation has a pair-breaking influence. The energy gap and depend very sensitively on U, V and band filling n and develop a maximum away from half filling as function of n. The ratio varies with n, being higher than the BCS value near half filling and reaching the BCS value for lower n. Received 17 February 1999     

From independent particle towards collective motion for two polarized electrons on a square lattice

The two dimensional crossover from independent particle towards collective motion is studied using 2 polarized electrons (spinless fermions) interacting via a U/r Coulomb repulsion in a L×L square lattice with periodic boundary conditions and nearest neighbor hopping t. Three regimes characterize the ground state when U/t increases. Firstly, when the fluctuation Δr of the spacing r between the two particles is larger than the lattice spacing a, there is a scaling length L ₀ = π²(t/U) such that the relative fluctuation Δr/〈r〉 is a universal function of the dimensionless ratio L/L ₀, up to finite size corrections of order L^-2. L < L ₀ and L > L ₀ are respectively the limits of the free particle Fermi motion and of the correlated motion of a Wigner molecule. Secondly, when U/t exceeds a threshold U ^*(L)/t, Δr becomes smaller than a, giving rise to a correlated lattice regime where the previous scaling breaks down and analytical expansions in powers of t/U become valid. A weak random potential reduces the scaling length and favors the correlated motion. Received 28 March 2002 Published online 19 November 2002     

Flow to strong coupling in the two-dimensional Hubbard model

We extend the analysis of the renormalization group flow in the two-dimensional Hubbard model close to half-filling using the recently developed temperature flow formalism. We investigate the interplay of d-density wave and Fermi surface deformation tendencies with those towards d-wave pairing and antiferromagnetism. For a ratio of next nearest to nearest neighbor hoppings, t'/t = - 0.25, and band fillings where the Fermi surface is inside the Umklapp surface, only the d-pairing susceptibility diverges at low temperatures. When the Fermi surface intersects the Umklapp surface close to the saddle points, d-wave pairing, d-density wave, antiferromagnetic and, to a weaker extent, d-wave Fermi surface deformation susceptibilities grow together when the interactions flow to strong coupling. We interpret these findings as indications for a non-trivial strongly coupled phase with short-ranged superconducting and antiferromagnetic correlations, in close analogy with the spin liquid ground state in the well-understood two-leg Hubbard ladder. Received 23 January 2002     

Dynamical mean-field theory of a simplified double-exchange model

Simplified double-exchange model including transfer of the itinerant electrons with spin parallel to the localized spin in the same site and the indirect interaction J of kinetic type between localized spins is comprihensively investigated. The model is exactly solved in infinite dimensions. The exact equations describing the main ordered phases (ferromagnetic and antiferromagnetic) are obtained for the Bethe lattice with (z is the coordination number) in analytical form. The exact expression for the generalized paramagnetic susceptibility of the localized-spin subsystem is also obtained in analytical form. It is shown that temperature dependence of the uniform and the staggered susceptibilities has deviation from Curie-Weiss law. Dependence of Curie and Néel temperatures on itinerant-electron concentration is discussed to study instability conditions of the paramagnetic phase. Anomalous temperature behaviour of the chemical potential, the thermopower and the specific heat is investigated near the Curie point. It is found for J=0 that the system is unstable towards temperature phase separation between ferromagnetic and paramagnetic states. A phase separation connected with antiferromagnetic and the paramagnetic phases can occur only at . Zero-temperature phase diagram including the phase separation between ferromagnetic and antiferromagnetic states is given. Received 28 May 1999 and Received in final form 14 July 1999     

混合自旋(S=1,1/2)模型具有再次近邻反铁磁相互作用晶格基态

本文发展文献[1]的方法到两种不同自旋的原子(S_a=1,S_b=1/2)构成的晶格中,计算了简单立方晶格在具有再次近邻反铁磁相互作用下在外磁场中的基态自旋结构、能量和相界。从文中给出的相图可知:这种晶格有两种反铁磁自旋结构,有四种亚铁磁自旋结构。 关键词：     

Spin coupling and magnetic field effects on the finite-size free energy and its non-extensivity for 1-D Ising model with nearest and next-nearest neighbor interactions in nanosystem

The effects of second-neighbor spin coupling interactions and a magnetic field are investigated on the free energies of a finite-size 1-D Ising model. For both ferromagnetic of nearest neighbor (NN) and next-nearest neighbor (NNN) spin coupling interactions, the finite-size free energy first increases and then approaches a constant value for any size of the spin chain. In contrast, when NNN and NN spin coupling interactions are antiferromagnetic and ferromagnetic, respectively, the finite-size free energy gradually decreases by increasing the competition factor and eventually vanishes for large values of it. When a magnetic field is applied, the finite-size free energy decreases with respect to the case of zero magnetic fields for both ferromagnetic and antiferromagnetic spin coupling interactions. Deviation of free energy per size for finite-size systems relative to the infinite system increases when the spin coupling interactions as well as the f parameter (the ratio of the magnetic field to NN spin coupling interaction) increase.